Examples

While we present core functionality in the User Guide, we here provide several examples along with XDiag to demonstrate how we can build more advanced applications from these basic building blocks. The examples are provided in the directory examples in the C++ source code directory, and can be compiled using CMake.

cmake -S . -B build -D BUILD_EXAMPLES=On
cmake --build build

The executables are then available in the directory build/examples. Most examples are also provided as a Julia script, and visualization scripts for the results are available.

Ground states

• Ground state energy

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  Computes the ground state energy of a simple Heisenberg spin \(S=1/2\) chain

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• Ground state correlators

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  Computes ground state correlators of a simple Heisenberg spin \(S=1/2\) chain with the help of symmetries.

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• Entanglement entropy ground state

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  Computes ground state entanglement entropy of an XXZ spin \(S=1/2\) chain.

  

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• CDW in attractive Hubbard model

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  Computes charge correlations in the ground state of the attractive 2D Hubbard model.

  

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• Kitaev-Heisenberg honeycomb model

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  Computes the ground state of the Heisenberg-Kitaev model throughout its phase diagram

  

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Full exact diagonalization

• Specific heat random t-J model

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  Computes the specific heat of the random t-J model via full ED over multiple disorder realizations.

  

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• Specific heat triangular t-J model

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  Computes the specific heat of the triangular t-J model via full ED.

  

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• Spin chain level statistics

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  Demonstrates Poissonian and Wigner-Dyson level statistics of integrable and non-integrable spin chains, respectively.

  

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• Many-body localization

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  Studies hallmark diagonstics of a many-body localized system.

  

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Tower of States

• TOS \(\alpha \text{XX}\) chain

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  Performs a tower of states analysis for the \(\alpha \text{XX}\) chain.

  

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• Heisenberg chain momentum resolved

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  Performs a (momentum) tower of states analysis for the antiferromagnetic chain.

  

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• Square lattice Heisenberg model

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  Performs a tower of states analysis for the Heisenberg model in the square lattice.

  

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• \(J_1 - J_2\) model triangular lattice

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  Performs a tower of states analysis for the \(J_1 - J_2\) model in the triangular lattice.

  

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• \(J_1 - J_2 - J_3\) Model in the kagome lattice

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  Performs a tower of states analysis for an extended kagome lattice Heisenberg antiferromagnet.

  

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• Attractive Hubbard model

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  Performs a tower of states analysis for the superconducting state in the attractive Hubbard model.

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Dynamical spectral functions

• Spin structure factor

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  Computes the dynamical spin structure factor of a spin \(S=1/2\) chain

  

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• Green's function

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  Computes the Green's function in a 2D Hubbard model

  

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• Optical conductivity

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  Computes the optical conductivity of one hole in a t-J model.

  

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Time Evolution

• Domain wall dynamics

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  Demonstrates the time evolution of a domain wall in the \(S=1/2\) XXZ chain.

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• Slow quench

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  Demonstrates the implementation of slow quench in the \(S=1/2\) Ising chain.

  

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• Hubbard interaction quench

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  Demonstrates the implementation of an interaction quench in the 2D Hubbard model.

  

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Thermodynamics

• Specific heat Shastry-Sutherland

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  Computes the specific heat using the TPQ states (finite temperature Lanczos method) for the Shastry Sutherland model.

  

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• Wilson ratio \(J_1\)-\(J_2\) square lattice

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  Computes the Wilson ratio using the TPQ states (finite temperature Lanczos method) for the \(J_1\)-\(J_2\) model on the square lattice

  

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